Cohn resigned earlier Tuesday amid a dispute with Trump over trade policy. Cohn had been trying to talk Trump out of a blanket 25 percent tariff on steel imports and a 10 percent tariff on aluminum imports, but the president has remained committed to the plan.

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During a joint press conference on Tuesday afternoon with Swedish Prime Minister Stefan Löfven, the president told reporters that "everybody" wants to work in his White House, despite a recent string of exits by high-level aides.

"The White House has tremendous energy, it has tremendous spirit. It is a great place to be working. Many, many people want every single job," Trump said.

"I could take any position in the White House and I'll have a choice of the 10 top people having to do with that position, everybody wants to be there," he added.